Yes in the sense that they both arise from the same effect, namely radiation emitted by an accelerating charge. Given by the Larmor formula for a nonrelativistic charge and the Lienard formula for a relativistic one.

However the term Bremsstrahlung is unfortunately used in situations which don't really deserve the term. Strictly speaking, Bremsstrahlung only applies to the deceleration of a charged particle entering matter, such as the slowing of an electron when it encounters an atom. The radiation emitted by particles in a particle accelerator is sometimes called Bremsstrahlung, but it ain't.